Related papers: Classical phase space singularities and quantizati…
It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in arXiv:2008.09387. In this paper, we start to extend this…
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics.…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
The Affine Coherent State Quantization procedure is applied to the case of a FRLW universe in the presence of a cosmological constant. The quantum corrections alter the dynamics of the system in the semiclassical regime, providing a…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of chaotic systems, and then it would be desirable that other classical invariants, not suffering from the same problem, could be used in the quantization of such…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
Levi-Civita spacetimes have both classical and quantum singularities. The relationship between the two is used here to study and clarify the physical aspects of the enigmatic Levi-Civita spacetimes.
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
We adopt the general formalism, which was developed in Paper I (arXiv:0708.1233) to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum field theory in time dependent…
The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The…
The classical and quantum properties of a new solution obtained in $2+1$% -dimensional gravity coupled with a real scalar field is analyzed in detail. The considered new solution is a one-parameter generalization of a previously known…